This invention relates to a technique for assessing the condition of a varying system such as a broadly-traded market, which may be a public financial market. More particularly, this invention is a technique for determining the state of a market price relative to a normative value, and whether such price is likely to change or to remain about the same.
It has been theorized that, absent undue influences, such as collusion within a market, price movements within that market should follow a normal distribution typical of purely random events. That is, it has been expected that if the frequency at which any given normalized or percentage price change occurs is plotted in a histogram as a function of price change, the result would be a Gaussian curve—i.e., the familiar bell curve represented by the formula:f(x)=(2πσ)−0.5exp(−((x−μ)2/2σ2)), −∞<x<∞The interpretation of such a curve in the context of, for example, the United States equity markets, as typified by the New York Stock Exchange, or other securities or contract markets, is that most often, price changes are zero—i.e., prices tend to remain where they are, small and moderate increases or decreases are the next most frequent occurrences, and very large increases or decreases are vanishingly rare.
Models used to predict stock market activity have tended to be based on the assumption that price change activity follows a normal distribution.
However, empirical observations show that the actual curve is a distorted bell curve. Specifically, the peak is taller than expected, meaning prices stay about the same even more often than would be expected from purely random changes, and narrower than expected, meaning that the frequency of moderate increases or decreases is less than expected, and the “tails” of the curve—in the ranges that would be expected to be statistically insignificant—have unexpected bulges, meaning that extreme increases and decreases happen more frequently than expected.
These variations of market behavior from expected norms lead to the failure of the known models for market assessment and prediction.
It would be desirable to be able to develop a model of market price change activity that explains the non-normal price change distribution of such activity, and to provide a technique for market assessment and prediction based on such a model.